Direct GBQ Algorithm for Solving Mixed Trigonometric Polynomial Systems
Received:January 05, 2016  Revised:May 06, 2016
Key Word: mixed trigonometric polynomial system   polynomial system   homotopy method   GBQ algorithm   upper bound  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11101067; 11171051) and the Fundamental Research Funds for the Central Universities (Grant No.DUT16LK04).
Author NameAffiliation
Yan YU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China; College of Sciences, Shenyang Agricultural University, Liaoning 110866, P. R. China 
Bo DONG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Bo YU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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Abstract:
      In many fields of science and engineering, it is needed to find all solutions of mixed trigonometric polynomial systems. Commonly, mixed trigonometric polynomial systems are transformed into polynomial systems by variable substitution and adding some quadratic equations, and then solved by some numerical methods. However, transformation of a mixed trigonometric polynomial system into a polynomial system will increase the dimension of the system and hence induces extra computational work. In this paper, we consider to solve the mixed trigonometric polynomial systems by homotopy method directly. Homotopy with the start system constructed by GBQ-algorithm is presented and homotopy theorems are proved. Preliminary numerical results show that our constructed direct homotopy method is more efficient than the existent direct homotopy methods.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.02.001
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